If \(10^{0.36}=x\), \(10^{0.81}=y\) and \(x^z=y^2\), then find the value of \(z\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.5
When both sides are written as powers of the same base, the exponents must be equal. Here the base is 10, and \(\left(10^m\right)^n=10^{mn}\).
\(x^z=\left(10^{0.36}\right)^z=10^{0.36z}\)
\(y^2=\left(10^{0.81}\right)^2=10^{1.62}\)
\(0.36z=1.62\)
\(z\displaystyle=\frac{1.62}{0.36}=4.5\)